Question: Simplify the following expression: $q = \dfrac{p^2 - 9p + 18}{p - 6} $
Solution: First factor the polynomial in the numerator. $ p^2 - 9p + 18 = (p - 6)(p - 3) $ So we can rewrite the expression as: $q = \dfrac{(p - 6)(p - 3)}{p - 6} $ We can divide the numerator and denominator by $(p - 6)$ on condition that $p \neq 6$ Therefore $q = p - 3; p \neq 6$